Electron dressing and photon probing 
So I have just gone over a lecture on electron dressing whereby an electron dresses itself in a foam of electrons/positrons/photons through photon emission and absorption (see image). 
My lecturer says something that I interpret to be along the lines of:

Probing with a photon with low $q$ (momentum) means you see all of the effects of the photon/electron/positron foam while probing with a high $q$ means you narrow in on the actual electron. 

However, does the probing photon not actually interact with the foam itself? How is this taken into account in distinguishing between the foam and actual electron?
This may be obvious but I am very new to particle physics. 
 A: 
Does the probing photon not actually interact with the foam itself?

The probing photon interacts with the virtual electron-positron pairs as well as with the real electron. It does not interact directly with the virtual photons.
Do you see how there is only one kind of vertex in these Feynman diagrams? You can draw a wavy line for the probing photon and connect it to any of the dark non-wavy lines representing electrons and positrons.
There are an infinite number of possible diagrams like this. Each one represents a contribution to the overall probability amplitude for the probing electron interacting with the real electron. The “virtual particles” are really just a convenient way to visualize and organize the complicated mathematics of how the two quantum fields (one for electrons and positrons, one for photons) interact.
“Virtual particles” are not like real particles because they don’t have the same relationship between energy, momentum, and mass that a real particle does. It’s best — despite their name — not to consider them particles at all, but just lines in Feynman diagrams and factors in probability amplitudes, parts of higher-order terms in a perturbative expansion of quantum field interactions.
